Dynamic side to side brake proportioning

ABSTRACT

A dynamic side-to-side braking method is disclosed. First, when the vehicle is in a combined braking and cornering maneuver, a desired braking force among tires of a vehicle is determined. Second, a brake force distribution of the desired braking force among the tires is determined. The brake force distribution is approximately proportional to a normal force distribution among the tires during the combined braking and cornering maneuver by the vehicle. When the vehicle excludes an active steering system, front or rear, the brake force distribution is determined as a function of a feedback correction to counterbalance a portion of a yaw moment experienced by the vehicle during the combined braking and cornering maneuver. When the vehicle includes an active steering system, front or rear, a steering correction is determined to counterbalance a portion of the yaw moment experienced by the vehicle during the combined braking and cornering maneuver.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention generally relates to control systems forautomotive vehicles. The present invention specifically relates to acontrol of a brake system of an automotive vehicle for improving vehicletransient and steady state performance in a combined braking andsteering maneuver by the vehicle, and an integrated control of a brakeand steering system of an automotive vehicle for improving vehicletransient and steady state performance in a combined braking andsteering maneuver by the vehicle.

[0003] 2. Description of the Related Art

[0004] Recently many vehicles have been produced with brake systemswhich can independently control brake forces (i.e., torques) ofindividual wheels. Many automakers and automotive suppliers are alsodeveloping brake by wire systems (e.g., electric or electro-hydraulic)which will give designers more freedom than ever before in controllingbraking forces of individual wheels in response to instantaneousconditions of motion as well as access to additional measured signals.At the same time, some vehicles are offered with active rear wheel steersystems, and an intense development efforts continue in the area ofaugmented front steer or steer by wire systems.

[0005] Most efforts in the area of brake control algorithms are focusedon improving brake control in an anti-lock braking system (ABS) mode ofoperation and a vehicle stability enhancement (VSE) mode of operation.These modes of operations are active only when a vehicle is at or veryclose to the limit of adhesion. During base braking, the brake forcedistribution typically used is symmetric left to right. Thus, it is notaffected by vehicle cornering and is optimized for straight linebraking. Therefore, transient response of many vehicles in combinedsteering and braking maneuvers is less than ideal with a tendency of thevehicle to oversteer and to prematurely enter into ABS mode of operationdue to reduced normal loads on the pair of inside tires.

[0006] More specifically, FIGS. 1A-1C illustrate the fundamentalphysical principles of a vehicle 10 in a combined braking and right handcornering maneuver. As shown in FIG. 1A, vehicle 10 is subjected to alongitudinal force FLO equaling m*a_(x) and a lateral inertial force FLAequaling m*a_(y), where m is a mass of vehicle 10, a_(x) is alongitudinal acceleration of vehicle 10, and a_(y) is a lateralacceleration of vehicle 10. A pitch and roll moment of vehicle 10 duringthe maneuver is due to the longitudinal force FLO and the lateralinertial force FLA in combination with various pitch forces PLF, PRF,PLR, and PRR, and various roll forces RLF, RRF, RLR, and RRR, applied toa left front tire 11 a, a right front tire 11 b, a left rear tire 11 c,and a right rear tire 11 d, respectively. The pitch and roll moment ofvehicle 10 is balanced by various normal forces NLF, NRF, NLR, and NRRbeing applied to left front tire 11 a, right front tire 11 b, left reartire 11 c, and right rear tire lid, respectively. As a result, a normalload distribution among tires 11 a-11 d is shifted from rear tires 11 cand 11 d to front tires 11 a and 11 b due to braking, and from insidetires 11 b and 11 d to outside tires 11 a and 11 c due to cornering.Consequently, as shown in FIG. 1B, left front tire 11 a carries thelargest normal load and right rear tire 11 d carries the smallest normalload.

[0007] The vectors of forces VLF, VRF, VLR, and VRR in the yaw(horizontal) plane of vehicle 10 developed by each tire 11 a-11 d,respectively, must remain within a corresponding friction circle 12 a-12d, respectively, whose radii are equal to products of a surfacecoefficient of adhesion μ and the corresponding normal force NLF-NRR. Iftires 11 a-11 d are on a relatively uniform surface, the maximumavailable tire forces in the yaw plane are approximately proportional tonormal forces NLF-NRR. With the brake proportioning techniques known inthe art, the brake forces on both sides of vehicle 10 are approximatelythe same. Thus, during braking, the friction potential of outside tires11 a and 11 c is underutilized while inside tires 11 b and 11 d enterABS too early. In a 3-channel system, an ABS mode is entered on bothrear wheels 11 c and 11 d simultaneously whereby a further reduction inlongitudinal forces is generated.

[0008] Another undesirable consequence of traditional brake forcedistribution during a braking and cornering maneuver is that vehicle 10exhibits a tendency to oversteer, especially under light to moderatebraking. FIG. 1C illustrates a simplified bicycle model of vehicle 10for explaining the aforementioned oversteer condition of vehicle 10.Prior to braking during a steady state cornering, a lateral forceF_(yfa) applied to a front axle (not shown) of vehicle 10 and a lateralforce F_(yra) applied to a rear axle (not shown) of vehicle 10 balanceeach other whereby a yaw moment MZ about a center of mass 13 of vehicle10 is approximately zero in accordance with the following equation [1]:

M _(z) =F _(yfa) *a−F _(yra) *b=0  [1]

[0009] where a is a longitudinal distance between the front axle andcenter of mass 13, and b is a longitudinal distance between the rearaxle and center of mass 13. Lateral force F_(yfa) and lateral forceF_(yra) correspond to side slip angles of front tire 11 a and rear tire11 c, respectively, with the side slip angle of front tire 11 a beinglarger than the side slip angle of rear tire 11 c.

[0010] When brakes are applied to front tire 11 a and rear tire 11 c,normal force NLF is increased on front tire 11 a and normal force NFR isreduced on rear tire 11 c. Thus, if the side slip angles of front tire11 a and rear tire 11 c were to be maintained, an increase in lateralforce F_(yfa) on the front axle that is nearly proportional to normalforce NLF would occur while a decrease in lateral force F_(yra) on therear axle that is nearly proportional to normal force NLR would occur.This imbalance between lateral force F_(yfa) and lateral force F_(yra)increases yaw moment MZ in accordance with the following equation [2]:

M _(z) =F _(yfa) *a−F _(yra) *b>0  [2]

[0011] Consequently, the yaw rate of vehicle 10 increases until a newsteady state is reached. Another effect of braking is a reduction oflateral force F_(yfa) and lateral force F_(yra) due to development oflongitudinal forces (not show). This effect produces an opposite resultthan illustrated in FIG. 1C, but the effect is significantly small forlight and moderate braking, and therefore the first effect dominates. Inthis new steady state, the side slip angle of rear tire 11 c is largerthan prior to braking and the slide slip angle of front tire 11 a islower than prior to braking. This is essentially one of the definitionsof vehicle oversteer.

[0012] There is therefore a need for a brake control method forovercoming the aforementioned shortcomings described herein. The presentinvention addresses this need.

SUMMARY OF THE INVENTION

[0013] The present invention provides a novel and unique method andsystem for improving vehicle transient and steady state performance in acombined braking and steering maneuver by using side to sideproportioning of braking forces during braking in a turn. Accordingly,the present invention applies to any brake system that provides means ofcontrolling brake forces among wheels in various proportions (e.g., ahydraulic brake system, an electric brake by wire system, and a hybridof a hydraulic brake system and an electric brake by wire system). Whilethe present invention is not limited to any particular implementationscenario, the intended area for implementing the present invention ismainly in the range of a performance envelope below the activation ofprior art brake control algorithms related to ABS and VSE.

[0014] One form of the present invention is a method of dynamicallycontrolling an operation of a vehicle during a combined braking andcornering maneuver by the vehicle. First, a desired brake force for aplurality of tires of the vehicle is determined. Second, a brake forcedistribution of the desired brake force among the plurality of tires isdetermined. The brake force distribution is approximately proportionalto a normal force distribution among the plurality of tires during thecombined braking and cornering maneuver.

[0015] A second form of the present invention is vehicle comprising aplurality of tires and a brake controller. The brake controller isoperable to determine a desired brake force for the tires during acombined braking and cornering maneuver by the vehicle. The brakecontroller is further operable to determine a brake force distributionof the desired brake force among the tires with the brake forcedistribution being approximately proportional to a normal forcedistribution among the plurality of tires during the combined brakingand cornering maneuver.

[0016] The foregoing forms, and other forms, features and advantages ofthe present invention will become further apparent from the followingdetailed description of the presently preferred embodiments, read inconjunction with the accompanying drawings. The detailed description anddrawings are merely illustrative of the present invention rather thanlimiting, the scope of the present invention being defined by theappended claims and equivalents thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

[0017]FIG. 1A is an illustration of various forces as known in the artthat are applied to a vehicle and tires of the vehicle during a righthand turning maneuver of the vehicle;

[0018]FIG. 1B is a vector diagram illustrating various vector forces asknown in the art that are experienced by the vehicle of FIG. 1A duringthe right hand turning maneuver;

[0019]FIG. 1C is an illustration of a bicycle model as known in the artof the FIG. 1A during the right hand turning maneuver;

[0020]FIG. 2A is an illustration of a vehicle in accordance with thepresent invention;

[0021]FIG. 2B is a block diagram illustrating a steer controller and abrake controller in accordance with the present invention;

[0022]FIG. 3 is a flow chart illustrating a dynamic braking method inaccordance with the present invention;

[0023]FIG. 4 is an illustration of a generation of a yaw moment during abraking and a cornering maneuver of the vehicle of FIG. 2A; and

[0024]FIG. 5 is flow chart illustrating a dynamic steering method inaccordance with the present invention.

DETAILED DESCRIPTION OF THE PRESENTLY PREFERRED EMBODIMENTS

[0025]FIGS. 2A and 2B illustrate a steering controller 40 and a brakecontroller 50 in accordance with the present invention as installed in avehicle 20 having a left front tire 21 a, a right front tire 21 b, aleft rear tire 21 c, and a right rear tire 21 d. Left front tire 21 aand right front tire 21 b are coupled to a front axle 22 a while leftrear tire 21 c and right rear tire 21 d are coupled to a rear axle 22 b.A conventional front steering actuator 23 a applies a steering angle toleft front tire 21 a and right front tire 21 b relative to front axle 22a in response to a reception of a front steering angle signal δ_(f)and/or a reception of a front steering correction signal Δδ_(ftot) fromsteering controller 40. A conventional rear steering actuator 23 bapplies a steering angle to left rear tire 21 c and right rear tire 21 drelative to rear axle 22 b in response to a reception of a rear steeringangle signal δ_(r) and/or a reception of a rear steering correctionsignal Δδ_(rtot) from steering controller 40.

[0026] Steering controller 40 conventionally provides front steeringangle signal 6 f to front steering actuator 23 a and rear steering anglesignal δ_(r) rear steering actuator 23 b in response to a reception of asteering angle signal δ_(s) from a conventional steering wheel sensor 25coupled to a steering wheel 24. As will be further described herein inconnection with FIG. 5, steering controller 40 provides front steeringcorrection signal Δδ_(ftot) to front steering actuator 23 a and rearsteering correction signal Δδ_(rtot) to rear steering actuator 23 b inresponse to a reception of either a left front braking signal F_(x) LF,a right front braking signal F_(x) RF, a left rear braking signal F_(x)LR, and a right rear braking signal F_(x) RR from brake controller 51,or a reception of a longitudinal acceleration signal ax from aconventional sensor 35 and a lateral acceleration signal a_(y) from aconventional sensor 36.

[0027] Steering controller 40 is an electronic circuit comprised of oneor more components that are assembled as a common unit. Alternatively,for the multiple component embodiments, one or more of these componentsmay be distributed throughout vehicle 20. Steering controller 40 may becomprised of digital circuitry, analog circuitry, or both (e.g. anapplication specific integrated circuit). Also, steering controller 40may be programmable, a dedicated state machine, or a hybrid combinationof programmable and dedicated hardware. All signals described herein canbe either in analog form or digital form. Thus, to implement theprincipals of the present invention, steering controller 40 can furtherinclude any control clocks, interfaces, signal conditioners, filters,Analog-to-Digital (A/D) converters, Digital-to-Analog (D/A) converters,communication ports, or other types of operators as would occur to thosehaving ordinary skill in the art.

[0028] In one embodiment, steering controller 40 includes one or morecentral processing units 41 operatively coupled to one or moresolid-state memory devices 42. Memory device(s) 42 contain programmingcorresponding to a flowchart 80 (FIG. 5) for implementing a dynamicside-to-side braking method of the present invention and is arranged forreading and writing of data in accordance with the principals of thepresent invention.

[0029] A conventional brake 26 a is coupled to left front tire 21 a witha conventional brake actuator 27 a applying a brake force via aconventional master cylinder 28 to left front tire 21 a in response to areception of left front braking signal F_(x) LF from brake controller50. A conventional brake 26 b is coupled to right front tire 21 b with aconventional brake actuator 27 b applying a brake force via mastercylinder 28 to right front tire 21 b in response to either a receptionof right front braking signal F_(x) RF from brake controller 50. Aconventional brake 26 c is coupled to left rear tire 21 c with aconventional brake actuator 27 c applying a brake force via mastercylinder 28 to left rear tire 21 c in response to a reception of leftrear braking signal F_(x) LR from brake controller 50. A conventionalbrake 26 d is coupled right rear tire 21 d with a conventional brakeactuator 27 d applying a brake force via master cylinder 28 to rightrear tire 21 d in response to a reception of right rear braking signalF_(x) RR from brake controller 50.

[0030] Brake controller 50 provides left front braking signal F_(x) LF,right front braking signal F_(x) RF, left rear braking signal F_(x) LR,and right rear braking signal F_(x) RR in response to either a receptionof a brake pedal switch signal BP_(s) from a conventional brake pedalswitch 30 coupled to brake pedal 29 and/or a reception of a brake pedalposition or brake pedal force signal BPP_(s) from a conventional brakepedal position or force sensor 31 coupled to brake pedal 29. Brakecontroller 50 receives additional signals indicative of variousoperative conditions of vehicle 20 to thereby determine the magnitudesof left front braking signal F_(x) LF, right front braking signal F_(x)RF, left rear braking signal F_(x) LR, and right rear braking signalF_(x) RR. Specifically, brake controller 50 receives a left front tirespeed signal V_(s) LF from a conventional speed sensor 32 a coupled toleft front tire 21 a. Brake controller 50 receives a right front tirespeed signal V_(s) RF from a conventional speed sensor 32 b coupled toright front tire 21 b. Brake controller 50 receives a left rear tirespeed signal V_(s) LR from a conventional speed sensor 32 c coupled toleft rear tire 21 c. Brake controller 50 receives a right rear tirespeed signal V_(s) RR from a conventional speed sensor 32 d coupled toright rear tire 21 d. Brake controller 50 also receives a brake fluidpressure signal BFP_(s) from a conventional brake fluid pressure sensor33 coupled to master cylinder 28, a yaw rate signal _(s) from aconventional yaw rate sensor 34, longitudinal acceleration signal axfrom sensor 35, and lateral acceleration signal a_(y) from sensor 36.

[0031] Brake controller 50 is an electronic circuit comprised of one ormore components that are assembled as a common unit. Alternatively, forthe multiple component embodiments, one or more of these components maybe distributed throughout vehicle 20. Brake controller 50 may becomprised of digital circuitry, analog circuitry, or both (e.g. anapplication specific integrated circuit). Also, brake controller 50 maybe programmable, a dedicated state machine, or a hybrid combination ofprogrammable and dedicated hardware. All signals described herein can bein analog form or in digital form. Thus, to implement the principals ofthe present invention, brake controller 50 can further include anycontrol clocks, interfaces, signal conditioners, filters,Analog-to-Digital (A/D) converters, Digital-to-Analog (D/A) converters,communication ports, or other types of operators as would occur to thosehaving ordinary skill in the art.

[0032] In one embodiment, brake controller 50 includes one or morecentral processing units 51 operatively coupled to one or moresolid-state memory devices 52. Memory device(s) 52 contain programmingcorresponding to flowchart 60 (FIG. 3) for implementing a dynamicside-to-side braking method of the present invention and is arranged forreading and writing of data in accordance with the principals of thepresent invention.

[0033] Steering controller 40 and brake controller 50 represent animprovement in a braking performance by vehicle 20 during a combinedcornering and braking maneuver through a new and unique utilization offrictional forces among tires 21 a-21 d. The primary principle of thepresent invention is to achieve a total brake force distribution ofbrake forces F_(x) LF-F_(x) RR among tires 21 a-21 d, respectively,during the combined cornering and braking maneuver that approximates atotal normal force distribution of a normal left front tire force NLF, anormal right front tire force NLF, a normal left rear tire force NLR,and a normal right rear tire force NRR in accordance with the followingequations [2a]-[2d], respectively:

N LF =m*g*b/(2*L)+M*a _(x) *h _(cg)/(2*L)+k _(rollf) *m*h _(cg) *a _(y)/t _(w)  [2a]

N RF =m*g*b/(2*L)+m*a _(x) *h _(cg)/(2*L)−k _(rollf) *m*h _(cg) *a _(y)/t _(w)  [2b]

N LR =m*g*a/(2*L)−m*a _(x) *h _(cg)/(2*L)+k _(rollr) *m*h _(cg) *a _(y)/t _(w)  [2c]

N RR =m*g*a/(2*L)−m*a _(x) *h _(cg)/(2*L)−k _(rollr) *m*h _(cg) *a _(y)/t _(w)  [2d]

[0034] where m is the total mass of vehicle 20, g is gravity, a is thedistance between front axle 22 a and the center of gravity of vehicle20, b is the distance between rear axle 22 b and the center of gravityof vehicle 20, L is a wheelbase of vehicle 10 equaling a distancebetween front axle 22 a and rear axle 22 b, h_(cg) is a height of acenter of gravity of vehicle 20 above ground, and t_(w) is track widthof front axle 22 a and rear axle 22 b. Symbol k_(rollf) denotes afraction of a total suspension roll stiffness contributed by a frontsuspension (not shown) of vehicle 20, and k_(rollr)=1−k_(rollf) is thefraction of total roll stiffness contributed by a rear suspension (notshown) of vehicle 20. In one embodiment, k_(rollf) is in accordance withthe following equation [3]:

k _(rollf)=κ_(f)/(κ_(f)+κ_(r))  [3]

[0035] where κ_(f) and κ_(r) are the nominal roll stiffness of the frontsuspension and the rear suspension, respectively. In equations[2a]-[2d], m*g*a/(2*L) and m*g*b/(2*L) represent the static normal loadon the corresponding tire, m*a_(x)*h_(cg)/(2*L) represents a loadtransfer due to longitudinal acceleration ax which is assumed positiveduring braking, and k_(rollf)*m*h_(cg)*a_(y)/t_(w) andk_(rollr)*m*h_(cg)*a_(y)/t_(w) represent a load transfer due to lateralacceleration a_(y) which is positive in a right hand turn and negativein a left hand turn.

[0036]FIG. 3 illustrates a flowchart 60 implemented by brake controller50 during a combined cornering and braking maneuver of vehicle 20.During a stage S62 of flowchart 60, brake controller 50 filters andprocesses inputs from sensors 32 a-32 d, and 34-36. Specifically,vehicle left front tire speed signal V_(s) LF, vehicle right front tirespeed signal V_(s) RF, vehicle left rear tire speed signal V_(s) LR, andvehicle right rear tire speed signal V_(s) RR from sensors 32 a-32 d,respectively, are processed as known in the art to obtain a vehiclespeed signal V_(x). Yaw rate signal _(s), longitudinal accelerationsignal a_(x), and lateral acceleration signal a_(y) as well as vehiclespeed signal V_(x) are conditioned as required by the remaining stagesof flowchart 60.

[0037] Longitudinal acceleration signal ax and lateral accelerationsignal a_(y) are estimated in an embodiment of a vehicle in accordancewith the present invention that excludes sensor 35 and sensor 36.Longitudinal acceleration signal a_(x) can be estimated as a function ofbrake pedal position signal BPP_(s) and/or brake fluid pressure signalBFP_(s) as would occur to those having ordinary skill in the art.Lateral acceleration signal a_(y) can be estimated as a function ofsteering angle signal δ_(s) and vehicle speed signal V_(x). In oneembodiment, the following equation [4] is utilized to estimate a desiredlateral acceleration signal a_(ydes):

a _(ydes) =v _(x) ²*δ_(s)/(L+K _(u) *v _(x) ²)  [4]

[0038] where L is the wheelbase of vehicle 20 and K_(u) is theundersteer coefficient of vehicle 20. Another method of dynamicallydetermining the desired lateral acceleration signal a_(ydes) isdescribed in U.S. Pat. No. 5,931,887, which is hereby incorporated byreference. The magnitude of the desired lateral acceleration signala_(ydes) can be limited by a maximum lateral acceleration achievable ondry surface for vehicle 20 (e.g., approximately 8 m/s² when vehicle 20is a sedan).

[0039] Flowchart 60 proceeds to a stage S64 upon a completion of stageS62. During stage S64, a total desired brake force F_(xdestot) isdetermined. In one embodiment, as known in the art, total desired brakeforce F_(xdestot) is determined as a function of brake pedal positionsignal BPP_(s) and/or brake fluid pressure signal BFP_(s) as well as aconstant factor. The magnitude of total desired brake force F_(xdestot)can be limited by a maximum desired brake force. In a second embodiment,total desired brake force F_(xdestot) is determined by the followingequation [5]:

F _(xdestot) =m*a _(xdes)  [5]

[0040] Flowchart 60 proceeds to a stage S66 upon a completion of stageS64. During stage S66, a final brake force distribution of brake forcesF_(x) LF-F_(x) RR among tires 21 a-21 d, respectively, of vehicle 20 isdetermined. In one embodiment, brake forces F_(x) LF-F_(x) RR aredetermined in accordance with the following equations [6a]-[6d]:

F _(x) LF =m*a _(xdes*[b/)(2*L)+a _(x) *h _(cg)/(2*L*g)+η*k _(rollf) *h_(cg) *a _(y)/(t _(w) *g)]  [6a]

F _(x) RF =m*a _(xdes*[b/)(2*L)+a _(x) *h _(cg)/(2*L*g)−η*k _(rollf) *h_(cg) *a _(y)/(t _(w*g))]  [6b]

F _(x) LR =m*a _(xdes*[a/)(2*L)−a _(x) *h _(cg)/(2*L*g)+η*k _(rollr) *h_(cg) *a _(y)/(t _(w) *g)]  [6c]

F _(x) RR =m*a _(xdes*[a/)(2*L)−a _(x*) h _(cg)/(2*L*g)−η*k _(rollr) *h_(cg) *a _(y)/(t _(w) *g)]  [6d]

[0041] where a brake distribution factor η is a ratio of lateral loadtransfer among tires 21 a-21 d, and a magnitude of brake distributionfactor η varies from 0 to 1. Alternatively, programming within brakecontroller 50 corresponding to equations [6a]-[6d] can be replaced bylook up tables depending on longitudinal acceleration signal a_(x) andlateral acceleration signal a_(y).

[0042] From equations [6a]-[6d], when brake distribution factor η=1, thebrake force distribution of brake forces F_(x) LF-F_(x) RR isproportional to the distribution of normal forces NLF-NRR. When brakedistribution factor η=0, brake force F_(x) LF and brake force F_(x) RFare equal while brake force F_(x) LR and brake force F_(x) RR are equal.In one embodiment, brake force distribution factor η is a feed forwardcomponent that is a function of longitudinal acceleration signal a_(x)of vehicle 20. More specifically, brake distribution factor η equates anominal value (e.g., 1.0 for vehicles with active steering such asvehicle 20, and 0.6 for vehicles without active steering) whenlongitudinal acceleration signal axis less than or equal to 80% of amaximum longitudinal acceleration of vehicle 20 (e.g., approximately 10m/s²). Brake distribution factor η is linearly reduced as longitudinalacceleration signal a_(x) increases above 80% of a maximum longitudinalacceleration of vehicle 20 until brake distribution factor ηapproximates 0.2 lower than the nominal value (e.g., 0.8 for vehicleswith active steering such as vehicle 20, and 0.4 for vehicles withoutactive steering). The dynamic determination of brake distribution factorη prevents vehicle 20 from an oversteer during a light and moderatebraking in a turn while limiting an understeer of vehicle 20 during veryheavy braking in a turn. In another embodiment, brake distributionfactor η can be increased slightly as a function of a high vehicle speedV_(x) in order to promote understeer during braking in turn at highspeeds.

[0043] Flowchart 60 is terminated upon a completion of stage S66.

[0044]FIG. 4 illustrates a yaw moment ΔM_(z1) produced by differentialbraking in accordance with the final braking force distribution of F_(x)LF-F_(x) RR. Vehicle 20 is equipped with active steering system wherebythe final braking force distribution of F_(x) LF-F_(x) RR isproportional to the normal force distribution of NLF-NRR with an excessof yaw moment ΔM_(z1) being counterbalanced by lateral forces resultingfrom a steering correction of either front tires 21 a and 21 b and/orrear tire 21 c and 21 d as controlled by an implementation of aflowchart 80 by steering controller 40.

[0045]FIG. 5 illustrates flowchart 80. During a stage S82 of flowchart80, steering controller 40 filters and processes braking forcedistribution of F_(x) LF-F_(x) RR from brake controller 50. Steeringcontroller 40 proceeds to a stage S84 of flowchart 80 upon a completionof stage S82 to determine yaw moment ΔM_(z1) in accordance with thefollowing equation [7]:

ΔM _(z1)=(F _(x) LF −F _(x) RF +F _(x) LR −F _(x) RR)*t _(w)/2  [7]

[0046] Alternatively, yaw moment ΔM_(z) is determined in accordance withthe following equation [8]:

ΔM _(z1) =η*a _(xdes*a) _(y) *m*h _(cg) /g  [8]

[0047] In order to fully compensate yaw moment ΔM_(z1) by steering, ayaw moment ΔM_(z2) generated by the change in tire lateral forces due toinstantaneous change in the steering angle must be equal in magnitude,but opposite in sign, to yaw moment ΔM_(z1). Steering controller 40therefore proceeds to a stage S86 of flowchart 80 upon a completion ofstage S84 to determine either a front steering correction Δδ_(f) or arear steering correction Δδ_(r) as a function of yaw moment ΔM_(z1) inaccordance with the following equations [9a] and [9b], respectively:

Δδ_(f) =ΔM _(z1)/(2*C _(yf) *a)  [9a]

Δδ_(r) =−ΔM _(z1)/(2*C _(yr*b))  [9b]

[0048] where C_(yf) denote a front tire cornering stiffness coefficientsof front tires 21 a and 21 b, and C_(yr) denote a rear tire corneringstiffness coefficients of rear tires 21 c and 21 d. Alternatively, frontsteering correction Δδ_(f) and rear steering correction Δδ_(r) are bothdetermined as functions of yaw moment ΔM_(z1) in accordance with thefollowing equations [10a] and [10b], respectively:

Δδ_(f)=(ε*ΔM _(z1))/(2*C _(yf) *a)  [10a]

Δδ_(r)=(−ε*ΔM _(z1))/(2*C _(yr) *b)  [10b]

[0049] where ε constitutes a fraction yaw moment ΔM_(z1) having a rangeof 0<ε≦1. During operation of vehicle 20, cornering stiffness C_(yf) andcornering stiffness C_(yr) can vary with normal load and above all withthe side slip angle of tires 21 a-21 d, respectively. Thus, corneringstiffness C_(yf) and cornering stiffness C_(yr) may significantlydeviate from their nominal values. In general, cornering stiffnessC_(yf) and cornering stiffness C_(yr) decrease with an increase in tireslip angles which tend to increase with lateral acceleration of vehicle20, and/or steering angle of tires 21 a-21 d. Thus, for optimalperformance it is recommended that the values of the steering correctionfactor ε or the entire product be determined through vehicle tests as afunction of lateral acceleration signal a_(y). Typically, the factor εwill be constant (or nearly constant) for the range of lateralacceleration of vehicle 20 up to about 0.8 times the maximum lateralacceleration that vehicle 20 can generate on dry surface, and mayincrease somewhat after that. For the rear active steering control,factor ε may also increase with an increase in a longitudinaldeceleration of vehicle 20 or an increase in braking force, sincebraking reduces cornering stiffness of the rear axle as a result ofreduction in normal forces.

[0050] Steering controller 40 proceeds to a stage S88 of flowchart 80upon a completion of stage S86 to filter the feedforward front steeringcorrection Δδ_(f) and feedforward rear steering correction Δδ_(r). Inone embodiment, feedforward front steering correction Δδ_(f) andfeedforward rear steering correction Δδr are passed through a high passfilter in accordance with the following transfer function equation [11]:

G _(f)(s)=s/(s+a _(f))  [11]

[0051] where a_(f) is a filter parameter with a typical value of 0.4rad/s. This results a front filtered value Δδ_(rfilt) and a rearfiltered value Δδ_(ffilt) in accordance with the following time domainequations [12a] and [12b]:

Δδ_(ffilt)(t)=(1−a _(f) *t)*Δδ_(ffilt)(t−t)+Δδ_(f)(t)−Δδ_(f)(t−t)  [12a]

Δδ_(rfilt)(t)=(1−a _(f) *t)*Δδ_(rfilt)(t−t)+≢δr(t)−Δδ_(r)(t−t)  [12b]

[0052] where t refers to the present time instant and t is a samplinginterval.

[0053] Steering controller 40 proceeds to a stage S90 of flowchart 80upon a completion of stage S88 to determine a feedback front steeringcorrection Δδffb and a feedback rear steering correction Δδ_(rfb) asdescribed in U.S. Patent Application entitled “Integrated Control OfActive Tire Steer and Brakes” hereby incorporated by reference in itsentirety. Steering controller 40 proceeds to a stage S92 of flowchart 80upon a completion of stage S90 to determine a total front steeringcorrection Δδ_(ftot) and a total rear steering correction Δδ_(rtot) inaccordance with the following equations [13a] and [13b], respectively:

Δδ_(ftot)=Δδ_(ffilt)+Δδ_(ffb)  [13a]

Δδ_(rtot)=Δδ_(rfilt)+Δδ_(rfb)  [13b]

[0054] Steering controller 40 provides total front steering correctionΔδ_(ftot) and/or a total rear steering correction Δδ_(rtot) to actuators23 a and 23 b, respectively.

[0055] Flowchart 80 is terminated upon a completion of stage S92.

[0056] Flowchart 60 as shown in FIG. 3 includes optional stages S68 andS70 for vehicles without active steer control whereby a proposed side toside brake force distribution is less than proportional to the normalload transfer. During stage S68, yaw moment resulting from disturbances,parameter variations, and environmental variations is roughly balancedby a desired yaw moment ΔM_(zd) resulting in a total brake distributionfactor η_(tot) in accordance with the following equations [14]-[17]:

Δv _(lr) =K _(Ωp)(v _(x),μ)*(Ω_(d)−Ω)+K ₁₀₆ _(^(d)) (v_(x),μ)*d(Ω_(d)−Ω)/dt+K _(vyd)(v _(x),μ)*d(v _(yd) −v _(y))/dt  [14]

ΔM_(zd) =C _(x)*ΔV _(lr)/V _(x)  [15]

Δη=ΔM _(zd) *g/(a _(xdes) *a _(y) *m*h _(cg))  [16]

η_(tot)=η+Δη  [17]

[0057] where a plurality of control gains K_(Ω) _(^(p)) , K_(Ω) _(^(d)), and K_(vyd) are dependent upon vehicle speed signal v_(x), anestimated surface coefficient of adhesion μ, and a steer flag (over- orunder-steer); Ω_(d) is a desired yaw rate; v_(y) is a lateral velocityvy; vyd is a desired lateral velocity v_(y); and C_(x) is thelongitudinal stiffness of tires 21 a-21 d. The signal ΔV_(lr) denoting adesired difference in wheel speeds between left wheels and right wheelsmay be computed as described in U.S. Pat. No. 6,035,251, issued Mar. 7,2000, and entitled “Brake System Control method Employing Yaw Rate AndSlip Angle Control”, the entirety of which is hereby incorporated byreference.

[0058] In order to avoid division by zero in equation [16], themagnitudes of lateral acceleration a_(y) and longitudinal accelerationax are limited from below by constant values (e.g., 2 m/s²). Inaddition, the magnitude of the factor Δη is limited to a reasonablevalue Δη_(max) which is selected so that the total brake distributionfactor η_(tot) does not exceed the range of <0;1>.

[0059] Brake controller 50 proceeds to a stage S70 of flowchart 60 upona completion of stage S68 to determine a final brake force distributionas a function of total brake distribution factor η_(tot) in accordancewith the following equations [18a]-[18d]:

F _(x) LF =m*a _(xdes) *[b/(2*L)+a _(x) *h _(cg)/(2*L*g)+η_(tot) *k_(rollf) *h _(cg) *a _(y)/(t _(w) *g)]  [18a]

F _(x) RF =m*a _(xdes) *[b/(2*L)+a _(x) *h _(cg)/(2*L*g)−η_(tot) *k_(rollf) *h _(cg) *a _(y)/(t _(w) *g)]  [18b]

F _(x) LR =m*a _(xdes) *[a/(2*L)−a _(x) *h _(cg)/(2*L*g)+η_(tOt) *k_(rollr) *h _(cg) *a _(y)/(t _(w) *g)]  [18c]

F _(x) RR =m*a _(xdes) *[a/(2*L)−a _(x*h) _(cg)/(2*L*g)−η_(tot) *k_(rollr) *h _(cg) *a _(y)/(t _(w) *g)]  [18d]

[0060] Flowchart 60 is terminated upon a completion of stage S70.

[0061] From the description herein of the present invention, thosehaving ordinary skill in the art will appreciate stages S62-S66 offlowchart 60 represent a feedforward control method which is effectivein nominal conditions. In order to achieve robustness of performance ofvehicle 20 with respect to changes in vehicle parameters (e.g., payload,a road surface coefficient of adhesion, road roughness, etc.,) afeedback control loop is introduced. Flowchart 80 represents a feedbackcontrol loop for vehicle 20 whereby any required correction in a yawresponse of vehicle 20 is achieved by changes in the steering angle offront tires 21 a and 21 b and/or rear tires 21 c and 23 d. Stages S62,S64, S68, and S70 of flowchart 60 represent a feedback control loop forvehicles in accordance with the present invention only having an activebrake control system whereby brake distribution factor is increased whensuch a vehicle is in oversteer and is decreased when such a vehicle isin understeer.

[0062] Those having ordinary skill in the art will also appreciatevarious advantages of the present invention. One advantage is animprovement in a utilization of a friction potential of all vehicletires, especially of the outside tires in a combined braking andcornering maneuver. A second advantage is an improvement in a trade offbetween vehicle cornering ability (i.e., lateral acceleration) anddeceleration (i.e., longitudinal deceleration) in a combined braking andcornering maneuver. A third advantage is an achievement of a neutralhandling behavior of the vehicle either by side to side proportioning orby side to side proportioning combined with steering correction. Afourth advantage is a less steering correction required by a driver tomaintain vehicle on desired path in a combined braking and corneringmaneuver. A fifth advantage is a delayed entry or no need for entry intoABS or Traxxar modes during a combined braking and cornering maneuver. Asixth advantage is a robustness with respect to parameter andenvironmental variations achieved through closed loop control. A seventhadvantage is an improvement in stopping distances on inclined roads.

[0063] While the embodiments of the present invention disclosed hereinare presently considered to be preferred, various changes andmodifications can be made without departing from the spirit and scope ofthe invention. The scope of the invention is indicated in the appendedclaims, and all changes that come within the meaning and range ofequivalents are intended to be embraced therein.

I claim:
 1. A method of dynamically controlling an operation of avehicle during a combined braking and cornering maneuver by the vehicle,said method comprising: determining a desired brake force for aplurality of tires of the vehicle; and determining a brake forcedistribution of the desired brake force among the plurality of tires,the brake force distribution being approximately proportional to anormal force distribution among the plurality of tires during thecombined braking and cornering maneuver.
 2. The method of claim 1,further comprising: operating a braking system of the vehicle inaccordance with a determination of the brake force distribution.
 3. Themethod of claim 2, further comprising: determining a steering correctionto counterbalance at least a portion of a yaw moment experienced by thevehicle during the combined braking and cornering maneuver.
 4. Themethod of claim 3, further comprising: operating a steering system ofthe vehicle as a function of the steering correction.
 5. The method ofclaim 1, further comprising: determining a braking correction as afunction of the desired brake force to counterbalance at least a portionof a yaw moment experienced by the vehicle during the combined brakingand cornering maneuver, wherein the brake force distribution isdetermined as a function of the braking correction.
 6. The method ofclaim 5, further comprising: operating the braking system in accordancewith a determination of the brake force distribution.
 7. A vehicle,comprising: a plurality of tires; and a brake controller, wherein saidbrake controller is operable to determine a desired brake force for saidplurality of tires during a combined braking and cornering maneuver bysaid vehicle, and wherein said brake controller is further operable todetermine a brake force distribution of the desired brake force amongsaid plurality of tires, the brake force distribution beingapproximately proportional to a normal force distribution among saidplurality of tires during the combined braking and cornering maneuver.8. The vehicle of claim 7, further comprising: braking system operableto apply a braking force to each tire of said plurality of tires inaccordance with a determination of the brake force distribution by saidbrake controller.
 9. The vehicle of claim 8, further comprising: asteering controller operable to determine a steering correction to oneor more tires of said plurality of tires to counterbalance at least aportion of a yaw moment experienced by the vehicle during the combinedbraking and cornering maneuver.
 10. The vehicle of claim 9, furthercomprising: a steering system operable to apply the steering correctionto one or more tires of said plurality of tires.
 11. The vehicle ofclaim 8, wherein said brake controller is further operable to determinea braking correction as a function of the desired brake force tocounterbalance at least a portion of a yaw moment experienced by thevehicle during the combined braking and cornering maneuver, and whereinsaid brake controller is further operable to determine the brake forcedistribution as a function of the braking correction.
 12. The vehicle ofclaim 11, wherein said braking system is operated in accordance with adetermination of the brake force distribution during the combinedcornering and braking maneuver.
 13. A vehicle, comprising: a pluralityof tires; and a brake controller including means for determining adesired brake force for said plurality of tires during a combinedbraking and cornering maneuver by said vehicle, and means fordetermining a brake force distribution of the desired brake force amongsaid plurality of tires, the brake force distribution beingapproximately proportional to a normal force distribution among saidplurality of tires during the combined braking and cornering maneuver.14. The vehicle of claim 13, further comprising: a braking systemoperable to apply a braking force to each tire of said plurality oftires in accordance with a determination of the brake force distributionby said brake controller.
 15. The vehicle of claim 14, furthercomprising: a steering controller including means for determining asteering correction to one or more tires of said plurality of tires tocounterbalance at least a portion of a yaw moment experienced by thevehicle during the combined braking and cornering maneuver.
 16. Thevehicle of claim 15, further comprising: a steering system operable toapply the steering correction to one or more tires of said plurality oftires.
 17. The vehicle of claim 14, wherein said brake controllerfurther includes means for determining a braking correction as afunction of the desired brake force to counterbalance at least a portionof a yaw moment experienced by the vehicle during the combined brakingand cornering maneuver.
 18. The vehicle of claim 17, wherein saidbraking system is operated in accordance with a determination of thebrake force distribution during the combined cornering and brakingmaneuver.
 19. The vehicle of claim 14, further comprising: a steeringcontroller including means for determining a yaw moment generated by adifferential braking of said braking system; means for determining afeedforward steering correction as a function of the yaw moment; meansfor filtering the feedforward steering correction; means for determininga feedback steering correction as a function of the feedforward steeringcorrection upon a filtering of the feedforward steering correction; andmeans for determining a steering correction as a function of thefeedforward steering correction and the feedback steering correction.20. The vehicle of claim 19, further comprising: a steering systemoperable to apply the steering correction to one or more tires of saidplurality of tires.